Are a RJ11 jack and a RJ45 socket physically compatible?

Yes it can. I have my home ADSL modem line (RJ-11) plugged into an RJ-45 socket, which goes back to my BT master socket.

They are fiddly to unplug though.

Like others have said about alignment problems, be mindful of this. The outer edges of the RJ11 cable end are thick plastic and will push the copper connectors in positions 2 and 7 down further then they are supposed to go which can cause a later issue with a RJ45 in it's place.

Yes, you could do this. You can wire RJ-45 to handle RJ-11 signals.

Personally I'd tend to look at just a few jacks with this setup as a bit unprofessional, but I've seen installations where they did everything as RJ-45 to avoid needed two kinds of connectors/cabling/etc.